论文标题
解决有关烷基维纳（Wiener）极性指数的极端问题的解决方案
Towards the Solution of an Extremal Problem Concerning the Wiener Polarity Index of Alkanes
论文作者
论文摘要
Wiener Polarity指数$ W_P $是研究最多的分子结构描述之一，是由化学家Harold Wiener设计的，原因是预测了烷烃的沸点。用于化学树的索引$ W_P $（代表烷烃的化学图）定义为距离3的无序对顶点的数量。具有至少3个学位的化学树的顶点称为分支顶点。化学树$ t $的一部分是一个路径subtree $ s $，其终端顶点的学位不同于2 $ t $，每个内部顶点（如果存在）$ s $的$ s $具有2级的$ t $。在本文中，Wiener Polarity指数$ W_P $的最佳尖锐上限和下限是针对具有给定数量的分支顶点或细分市场的订单$ n $的化学树，并且表征了相应的极端化学树。由于派生结果，解决了有关具有固定数量段或分支顶点的化学树值的最大$ W_P $值的开放问题。
The Wiener polarity index $W_p$, one of the most studied molecular structure descriptors, was devised by the chemist Harold Wiener for predicting the boiling points of alkanes. The index $W_p$ for chemical trees (chemical graphs representing alkanes) is defined as the number of unordered pairs of vertices at distance 3. A vertex of a chemical tree with the degree at least 3 is called a branching vertex. A segment of a chemical tree $T$ is a path-subtree $S$ whose terminal vertices have degrees different from 2 in $T$ and every internal vertex (if exists) of $S$ has degree 2 in $T$. In this paper, the best possible sharp upper and lower bounds on the Wiener polarity index $W_p$ are derived for the chemical trees of order $n$ with a given number of branching vertices or segments, and the corresponding extremal chemical trees are characterized. As a consequence of the derived results, an open problem concerning the maximal $W_p$ value of chemical trees with a fixed number of segments or branching vertices is solved.
